What is Line?
Show Hint
- Distance between three dots
- Distance between two dots
- Straight line
- None of these
The Correct Option is C
Solution and Explanation
Step 1: Understanding the definition of a line
A line is a geometric figure that extends in both directions infinitely and has no endpoints.
It is typically defined as the path traced by a moving point in a single direction.
Step 2: What is the minimum number of points to define a line?
A line can be defined using any two points.
Once we have two points, a straight line can be drawn connecting them.
Step 3: Evaluating the options
(A) Distance between three dots $\Rightarrow$ A curve can pass through three points; not necessarily a line.
(B) Distance between two dots $\Rightarrow$ This defines a line segment, not an infinite line.
(C) Straight line $\Rightarrow$ This is the correct conceptual and geometric definition.
(D) None of these $\Rightarrow$ Incorrect, as (C) is correct.
\[
\boxed{\text{Correct Answer: (C) Straight line}}
\]
Top Questions on Lines
- The line \( x = 1 + 5\mu, y = -5 + \mu, z = -6 - 3\mu \) passes through which of the following points?
Self-study helps students to build confidence in learning. It boosts the self-esteem of the learners. Recent surveys suggested that close to 50% learners were self-taught using internet resources and upskilled themselves.
A student may spend 1 hour to 6 hours in a day in upskilling self. The probability distribution of the number of hours spent by a student is given below: \[ P(X = x) = \begin{cases} kx^2, & \text{for } x = 1, 2, 3, \\ 2kx, & \text{for } x = 4, 5, 6, \\ 0, & \text{otherwise.} \end{cases} \] where \( x \) denotes the number of hours. Based on the above information, answer the following questions:
1. Express the probability distribution given above in the form of a probability distribution table.
2. Find the value of \( k \).
3. (a) Find the mean number of hours spent by the student. (b) Find \( P(1 < X < 6) \).- If the straight lines $ \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{-t} \quad \text{and} \quad \frac{x - 1}{t} = \frac{y - 4}{2} = \frac{z - 5}{1} \quad \text{are intersecting, then $ t $ can have:} $
- Find a unit vector in the direction of \( \overrightarrow{DA} \).
- If the lines \[ \frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2} \] and \[ \frac{x - 1}{3k} = \frac{y - 1}{1} = \frac{z - 6}{-7} \] are perpendicular to each other, find the value of \( k \) and hence write the vector equation of a line perpendicular to these two lines passing through the point \( (3, -4, 7) \).
Questions Asked in UP Board X exam
- If point $Q(0,1)$ is equidistant from points $P(5,-3)$ and $R(x,6)$, find the values of $x$.
- UP Board X - 2025
- Distance Formula
- (ii) What do you understand by Electrolytic refining? Explain with diagram.
- UP Board X - 2025
- Electrolytic Refining
- (iii) A refrigerator of 200 W is operated for 10 hours per day. Find out the cost of energy to operate it for 30 days at the rate of ₹6 per kWh.
- UP Board X - 2025
- Electrical Energy, Power
- (ii) What is the meaning of magnification produced by a lens? An object of length 5 cm is at a distance of 15 cm from a convex lens. Focal length of the lens is 10 cm. What will be the size of the image?
- UP Board X - 2025
- Linear magnification
$PQ$ is a chord of length $4\ \text{cm}$ of a circle of radius $2.5\ \text{cm}$. The tangents at $P$ and $Q$ intersect at a point $T$. Find the length of $TP$.
- UP Board X - 2025
- Tangent to a Circle